As an aircraft moves through the air, the wing is inclined to the
flight direction at some angle.
The angle between the chord
line of the airfoil and the flight direction is called the angle of
attack. Angle of attack has a large effect on the
lift
generated by a wing. During takes off, the pilot applies as much
thrust
as possible to make the airplane roll along launch rail. But
just before lifting off, the pilot "rotates" the aircraft. The nose
of the airplane rises, increasing the angle of attack and producing
the increased lift needed for takeoff.

The magnitude of the lift generated by
the wing depends on the
shape
of the wing and how it moves through
the air. For airfoils, the lift varies almost
linearly for small angles of attack (within +/- 10 degrees). For
higher inclinations, however, the dependence is quite complex. As an
object moves through the air, air molecules stick to the surface.
This creates a layer of air near the surface called a
boundary layer
that, in effect, changes the shape of the object. The flow
turning reacts to the edge of the boundary layer, just as it would to the
physical surface of an object. To make things more confusing, the
boundary layer may lift off or "separate" from the body and create an
effective shape much different from the physical shape. The
separation of the boundary layer explains why aircraft wings will
abruptly lose lift at high inclination to the flow. This condition was
called a stall when it was first encountered by the Wright brothers,
and that term still remains to this day.

On the slide shown above, the flow conditions for two airfoils are
shown on the left. The shape of the two foils is the same. The lower
foil is inclined at ten degrees to the incoming flow, while the upper
foil is inclined at twenty degrees. On the upper foil, the boundary
layer has separated and the wing is stalled. Predicting the stall
point (the angle at which the wing stalls) is very difficult
mathematically. Engineers
usually rely on wind
tunnel tests to determine the stall point. But this must be done
very carefully, matching all the important physical
parameters of the flow field.

The plot at the right of the figure shows how the lift varies with
angle of attack for a typical airfoil. At low angles, the lift is
nearly linear. Notice on this plot that at zero angle a small amount
of lift is generated because of the airfoil shape. If the airfoil had
been symmetric, the lift would be zero at zero angle of attack. At
the right of the curve, the lift changes rather abruptly and the
curve stops. In reality, you can set the airfoil at any angle you
want. However, once the wing stalls, the flow becomes highly
unsteady, and the value of the lift can change rapidly with time.
Because it is so hard to measure such flow conditions, engineers
usually leave the plot blank beyond wing stall.
You can generate your own plots of the lift versus angle of attack using
a computer simulation of the Wright's
1901 wind tunnel.

Since the amount of lift generated at zero angle and the location
of the stall point must usually be determined experimentally,
aerodynamicists include the effects of inclination in the lift
coefficient. For some simple examples, the lift coefficient can
be determined mathematically for small angles. (For thin airfoils at
subsonic speed, the lift coefficient is 2 x pi x angle, where pi is
3.1415926..., and the angle is given in radians {pi radians = 180
degrees}.) But in most cases, aerodynamicists rely on wind tunnel
testing and very sophisticated computer analysis to determine the
lift coefficient.

Let's investigate the dependence of lift on angle of attack using a Java
simulator.

Due to IT
security concerns, many users are currently experiencing problems running NASA Glenn
educational applets. The applets are slowly being updated, but it is a lengthy process.
If you are familiar with Java Runtime Environments (JRE), you may want to try downloading
the applet and running it on an Integrated Development Environment (IDE) such as Netbeans or Eclipse.
The following are tutorials for running Java applets on either IDE:
NetbeansEclipse

This page shows an interactive Java applet with flow past a airfoil. There
is a plotter and the calculated lift is displayed.

You can download your own copy of this applet by pushing the following button:

The program is downloaded in .zip format. You must save the file to disk and
then "Extract" the files. Click on
"Incline.html" to run the program off-line.

You can change the value of the angle of attack by using the
slider below the airfoil graphic, or by backspacing, typing in your value,
and hitting "Return" inside the input box next to the slider.
By using the drop menu labeled "Select Lift" you can choose to display
either the lift or lift coefficient on the graph.
You can perform the calculations in
either English or metric units by using the drop menu labeled "Select Units".
The red dot on the graph shows the current set of conditions.

As an experiment, set the angle to 5.0 degrees and note the amount of lift.
Now increase the angle to 10 degrees. Did the lift increase or decrease?
Increase the angle again to 15 degrees. What do you notice in the view window? Set the angle to 0 degrees. Is there any lift? What does this tell you
about the shape of the airfoil? Find the angle for which there is
no lift.